2 citations · 12 across the 11 of their papers we have counts for
11 papers
Jantzen Conjecture for singular characters
Wei Xiao
We show that the Jantzen filtration of a Verma module (possibly singular) coincides with its radical filtration. It implies that the Jantzen Conjecture on Verma modules holds for a…
Gelfand-Kirillov dimensions and associated varieties of highest weight modules
Zhanqiang Bai, Wei Xiao, Xun Xie
In this paper, we present a uniform formula of Lusztig's -functions on classical Weyl groups. Then we obtain an efficient algorithm for the Gelfand-Kirillov dimensions…
Jantzen coefficients and simplicity of generalized Verma modules
Wei Xiao, Ailin Zhang
The main purpose of the paper is to establish new tools in the study of . We introduce the Jantzen coefficients of generalized Verma modules. It comes fro…
Jantzen coefficients and radical filtrations for generalized Verma modules
Jun Hu, Wei Xiao
In this paper we give a sum formula for the radical filtration of generalized Verma modules in any (possibly singular) blocks of parabolic BGG category which can be viewed as a gen…
Blocks of the category in type
Jieren Hu, Wei Xiao, Ailin Zhang
In this paper, we determine the blocks of associated with semisimple Lie algebras of type .
Janzten coefficients and Blocks of category
Wei Xiao
The BGG category and its generalization play essential roles in representation theory and have led to far-reaching work. Some elementary pr…
Associated varieties of minimal highest weight modules
Zhanqiang Bai, Jia-Jun Ma, Wei Xiao +1
Let be a complex simple Lie algebra. A simple -module is called minimal if the associated variety of its annihilator ideal coincides with the closure o…
Dirac cohomology and Euler-Poincaré pairing for weight modules
Jingsong Huang, Wei Xiao
Let be a reductive Lie algebra over . For any simple weight module of with finite-dimensional weight spaces, we show that its Dirac cohomo…
Differential-operator representations of Weyl group and singular vectors
Wei Xiao
Given a suitable ordering of the positive root system associated with a semisimple Lie algebra, there exists a natural correspondence between Verma modules and related polynomial a…
Differential equations and singular vectors in Verma modules
Wei Xiao
Xu introduced a system of partial differential equations to investigate singular vectors in the Verma modules of highest weight over . He proved th…
Dirac operators and cohomology for Lie superalgebras
Wei Xiao
Vogan raised the idea of Dirac cohomology to study representations of semisimple Lie groups and Lie algebras. He conjectured that the infinitesimal character of Harish-Chandra modu…